I'd like this sort of thing restricted to a special effect (like the fountain jets, waterfalls, and so on). In my view it would be a looped animation based around an effect spawner that you could place basically anywhere. This would work for birds, butterflies, pond fish (such as koi), or really anything.
Planet Coaster had ambient pigeons flying around, but I believe I read somewhere that they were left out of zoo due to constraints on performance or something (this might have been a community theory rather than an official statement, it was a long time ago). Adding them in as special effects could at least provide players with the option.